In my opinion, the content of the song the woman sings (this is in Part II, Chapter 4) is symbolic of what it is that Winston feels is missing in his society. That is, I think, why he thinks that the Proles might be the hope for the future.

I know the song was written by a "versificator" machine, but its lyrics express things that Winston wants. He wants true feelings like the ones the woman sings about. He wants memories that will last across the years and not get changed by the Party.

When the woman sings those lyrics, I think Winston understands that his hopes are in the lyrics of the song. (It never says this in the book -- this is my interpretation of why the song matters.)